Studentized

In Linear Regression (Simple or Multiple), a residual is said to be :

• "Standardized" when it is divided by the square root of the data set estimated error variance.
• "Internally studentized" when it is divided by its own estimated standard deviation (recall that in linear regression, the variance of the residuals is not uniform even under the assumption of uniform error variance (homoskedasticity)).
• An "externally studentized" residual is the studentized residual of an observation with respect to the model built after discarding this observation from the data set.

As their name implies, studentized residuals follow (Student's) t distributions (when the errors are normally distributed). Studentized residuals play a central role in the definitions and properties of the classical detectors of observations having a particularly strong influence on the model predictions (e.g. DFFITS, Cook's distance). 

_______________________________________

Related readings :